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    Find General Solutions to a 2nd and 4th Order ODE

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    A) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t)

    b) y''+y=tcost

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    General solution to a 2nd + 4th order DE
    a) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t)
    Solution. The characteristic equation is

    Factoring it, we get

    So, we get

    So, the general solution to ODE: y'''' - 11y''' +45y"-81y'+54y =0 is

    where a,b,c and d are constants.

    Now in order to get the general solution to
    y'''' - 11y''' +45y"-81y'+54y = ...

    Solution Summary

    General Solutions to a 2nd and 4th Order ODE are found. The solution is detailed and well presented.